Higher June 2024 Paper 4 Q8
8 The price of a television is increased by 35%.
In a sale, the new price of the television is decreased by \(r\)%.
The overall percentage increase in the price of the television is 16.1%.
Find the value of \(r\).
You must show your working. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 14 with correct working | 5 | B4 for answer 0.14 with correct working or for answer 86 with correct working OR B3 for answer 0.86 with correct working | “Correct working” requires evidence of at least M2 Ignore % written on answer line and ignore × 100 and units when awarding M marks. Allow any correct method. |
| OR M4 for any correct calculation that would lead to 0.14 or 86 e.g. \(1 - \frac{1.161}{1.35}\) or \(\frac{135 - 116.1}{135}\) oe | M4 includes \(1 - \frac{1161}{1350}\) or \(\frac{1161}{1350} \times 100\) or \(\frac{1.35 - 1.161}{1.35}\) or \(\frac{1.161}{1.35} \times 100\) | ||
| OR M3 for any correct calculation that would lead to 0.86 e.g \(\frac{1.161}{1.35}\) or \(\frac{1161}{1350}\) oe | M3 includes \(\frac{116.1}{135}\) | ||
| OR M2 for 1.35 and 1.161 or 135 and 116.1 OR B1 for 1.35 or 135 or 1350 | M2 includes 1350 and 1161 or 1.35 – 1.161 or 1.161 – 1.35 or ±0.189 or [1]35 – [1]16.1 or 1.161 – 1.35 or ±18.9 B1 includes 1.161 or 116.1 or 1161 | ||
| If 0 or 1 scored, instead award SC3 for answer 14 with no working or insufficient working If 0 or 1 scored, instead award SC2 for answer 0.14 or 86 with no working or insufficient working If 0 scored, instead award SC1 for answer 0.86 with no working or insufficient working | Alternative method : e.g. trials needs M2 to award 5 marks, evidence of at least 2 trials seen or M1 for each correct trial up to M3, see appendix for figures | ||
Appendix: Question 8
| Price | increase | decrease | answer | |
|---|---|---|---|---|
| 100 | 135.00 | 1 | 133.65 | 116.10 |
| 135.00 | 2 | 132.30 | 116.10 | |
| 135.00 | 3 | 130.95 | 116.10 | |
| 135.00 | 4 | 129.60 | 116.10 | |
| 135.00 | 5 | 128.25 | 116.10 | |
| 135.00 | 6 | 126.90 | 116.10 | |
| 135.00 | 7 | 125.55 | 116.10 | |
| 135.00 | 8 | 124.20 | 116.10 | |
| 135.00 | 9 | 122.85 | 116.10 | |
| 135.00 | 10 | 121.50 | 116.10 | |
| 135.00 | 11 | 120.15 | 116.10 | |
| 135.00 | 12 | 118.80 | 116.10 | |
| 135.00 | 13 | 117.45 | 116.10 | |
| 135.00 | 14 | 116.10 | 116.10 | |
| 135.00 | 15 | 114.75 | 116.10 | |
| 135.00 | 16 | 113.40 | 116.10 | |
| 135.00 | 17 | 112.05 | 116.10 | |
| 135.00 | 18 | 110.70 | 116.10 | |
| 135.00 | 19 | 109.35 | 116.10 | |
| 135.00 | 20 | 108.00 | 116.10 | |
| 135.00 | 21 | 106.65 | 116.10 | |
| 135.00 | 22 | 105.30 | 116.10 | |
| 135.00 | 23 | 103.95 | 116.10 |